Related papers: A variational representation and large deviations …
Starting from the construction of a geometric rough path associated with a fractional Brownian motion with Hurst parameter $H\in]{1/4}, {1/2}[$ given by Coutin and Qian (2002), we prove a large deviation principle in the space of geometric…
We prove that a sequence of semi-discrete approximations converges to a multiplicative functional for reflected Brownian motion, which intuitively represents the Lyapunov exponent for the corresponding stochastic flow. The method of proof…
In this paper, we prove that there exists at least one solution for the reflected forward-backward stochastic differential equation driven by G-Brownian motion satisfying the obstacle constraint with monotone coefficients.
In this paper we prove, for small Hurst parameters, the higher order differentiability of a stochastic flow associated with a stochastic differential equation driven by an additive multi-dimensional fractional Brownian noise, where the…
We study some functional inequalities satisfied by the distribution of the solution of a stochastic differential equation driven by fractional Brownian motions. Such functional inequalities are obtained through new integration by parts…
By using the Picard iteration scheme, this article establishes the existence and uniqueness theory for solutions to stochastic functional differential equations driven by G-Browniain motion. Assuming the monotonicity conditions, the…
This paper develops a new technique for the path approximation of one-dimensional stochastic processes, more precisely the Brownian motion and families of stochastic differential equations sharply linked to the Brownian motion (usually…
We study well-posedness of sweeping processes with stochastic perturbations generated by a fractional Brownian motion and convergence of associated numerical schemes. To this end, we first prove new existence, uniqueness and approximation…
We study a stochastic recursive optimal control problem in which the cost functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Some of the economic and financial optimization…
We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some…
We prove a general functional limit theorem for multiparameter fractional Brownian motion. The functional law of the iterated logarithm, functional L\'{e}vy's modulus of continuity and many other results are its particular cases.…
The generalized fractional Brownian motion is a Gaussian self-similar process whose increments are not necessarily stationary. It appears in applications as the scaling limit of a shot noise process with a power law shape function and…
We prove a large deviation principle for the slow-fast rough differential equations under the controlled rough path framework. The driver rough paths are lifted from the mixed fractional Brownian motion with Hurst parameter $H\in…
Exact generalized stochastic representation of deterministic interaction between two dynamical (quantum or classical) systems is derived which helps when considering one of them to replace another by equivalent commutative ($c$-number…
We establish a large deviation principle for the process of the largest eigenvalue of an Hermitian Brownian motion. By a contraction principle, we recover the LDP for the largest eigenvalue of a rank one deformation of the GUE.
We prove that solutions of stochastic differential equations driven by fractional Brownian motion for $H>1/2$ define flows of homeomorphisms on $\mathbb{R}^{d}$.
We consider a generic diffusion on the 1D torus and give a simple representation formula for the large deviation rate functional of its invariant probability measure, in the limit of vanishing noise. Previously, this rate functional had…
Employing large deviation theory, we explore current fluctuations of underdamped Brownian motion for the paradigmatic example of a single particle in a one dimensional periodic potential. Two different approaches to the large deviation…
In this paper we consider the Allen-Cahn equation perturbed by a stochastic flux term and prove a large deviation principle. Using an associated stochastic flow of diffeomorphisms the equation can be transformed to a parabolic partial…
In this paper, we establish a large deviation principle for the solutions to the stochastic heat equations with logarithmic nonlinearity driven by Brownian motion, which is neither locally Lipschitz nor locally monotone. Nonlinear versions…